Optimization of generalized order-level inventory system under fully permissible delay in payment

¹ Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, India.
² Department of Mathematics, Sonarpur Mahavidyalaya, Kolkata, W.B., India.

^* Corresponding author: fuzzy_arindam@yahoo.com

Received: 3 March 2019
Accepted: 25 August 2019

Abstract

This article presents one generalized order-level inventory system with fully permissible delay in payment in various trade-credit intervals. Review of existing literature finds few EOQ models under simultaneous considerations of time-dependent generalized demand rate, time-dependent generalized rate of deterioration and time-dependent generalized backordering under fully permissible delay in payment. In those existing studies, the optimal inventory depletion time is independent of demand over the entire cycle. Here, present article frames one generalized order-level inventory system with fully permissible delay in payment across various trade-credit intervals. This finds that when the trade-credit period is longer than the inventory depletion time to settle the account, the optimal inventory depletion time is dependent of demand. Under this ambiance, one particular case having time-dependent ramp type demand rate, two variables time-dependent Weibull distribution rate of deterioration and time-dependent backordering rate with fully permissible delay in payment, finds that the optimal inventory depletion time varies inversely over demand in that period. Moreover, the proposed model shrinks to obtain many well-established EOQ models as the special cases to it. Next, a general algorithm determines the various optimal solutions corresponding to seven cases. The managerial insights extracted from sensitivity analysis of parameters include the suggestion to halt the promotional activities so as to foreshorten the demand in shortage period. Also, this analysis attests that the longer waiting period of retailers should be counterbalanced with various promotional activities and anticipated benefits.